Solve for $x$ and $y$ using elimination. ${-2x-6y = -64}$ ${3x-5y = -44}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $2$ ${-6x-18y = -192}$ $6x-10y = -88$ Add the top and bottom equations together. $-28y = -280$ $\dfrac{-28y}{{-28}} = \dfrac{-280}{{-28}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-2x-6y = -64}\thinspace$ to find $x$ ${-2x - 6}{(10)}{= -64}$ $-2x-60 = -64$ $-2x-60{+60} = -64{+60}$ $-2x = -4$ $\dfrac{-2x}{{-2}} = \dfrac{-4}{{-2}}$ ${x = 2}$ You can also plug ${y = 10}$ into $\thinspace {3x-5y = -44}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(10)}{= -44}$ ${x = 2}$